The problem addressed in this paper-the linehaul-feeder vehicle routing problem with virtual depots (LFVRP-VD)-can be regarded as an extension of the vehicle routing problem. During delivery operation, one large vehicle departs from the physical depot (PD) and services all virtual depots (VDs). A set of small vehicles delivers to customers and, if necessary, reloads either from the PD or from the large vehicle at a VD before continuing work. The objective of the operation is to minimize the total travel and waiting costs for all vehicles. Two heuristics that embed the cost-sharing method and the threshold method are proposed for initial solution construction. Seventeen test problems are extensively examined. The results show that the cost-sharing method outperforms the threshold method in terms of several selected performance measures. In addition, the more candidates available a VD can choose, the better the obtained objective value.
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Chen et al. (2011) studied this question.
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